{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Comparing DMD and KDMD for Slow manifold dynamics\n",
    "\n",
    "Here we consider perhaps one of the most widely known classic example of Koopman decomposition: a nonlinear system with a fast and slow manifold:\n",
    "\n",
    "$$\n",
    "\\dot{x}_1 = \\mu x_1 \\\\\n",
    "\\dot{x}_2 = \\lambda (x_2-x_1^2)\n",
    "$$\n",
    "where $\\mu=-0.05, \\lambda=-1$. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../src')"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import matplotlib.cm as cm\n",
    "\n",
    "import pykoopman as pk\n",
    "from scipy.integrate import odeint\n",
    "from scipy.stats.qmc import Sobol"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we generate the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(-0.9, 0.9)"
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = -0.05\n",
    "lda = -1.0\n",
    "def slow_manifold(x, t, mu, lda):\n",
    "    x1, x2 = x\n",
    "    dxdt = [mu*x1, \n",
    "            lda*(x2-x1*x1)]\n",
    "    return dxdt\n",
    "\n",
    "n_t = 40\n",
    "t = np.linspace(0, 20, n_t,endpoint=False)\n",
    "\n",
    "# use quasi-random for generating samples\n",
    "sampler=Sobol(d=2)\n",
    "\n",
    "\n",
    "x_list = []\n",
    "x_next_list = []\n",
    "plt.figure(figsize=(6,6))\n",
    "# for x0 in sampler.random(10)-0.5:\n",
    "#     sol = odeint(slow_manifold, x0, t, args=(mu,lda))\n",
    "#     plt.plot(sol[:,0],sol[:,1],'o-',lw=2,alpha=0.3)\n",
    "    \n",
    "#     x_list.append(sol[:-1])\n",
    "#     x_next_list.append(sol[1:])\n",
    "\n",
    "x0 = [0.3,0.5]\n",
    "sol = odeint(slow_manifold, x0, t, args=(mu,lda))\n",
    "plt.plot(sol[:,0],sol[:,1],'o-',lw=2,alpha=0.3)\n",
    "x_list.append(sol[:-1])\n",
    "x_next_list.append(sol[1:])\n",
    "\n",
    "x0 = [-0.7,0.3]\n",
    "sol = odeint(slow_manifold, x0, t, args=(mu,lda))\n",
    "plt.plot(sol[:,0],sol[:,1],'o-',lw=2,alpha=0.3)\n",
    "x_list.append(sol[:-1])\n",
    "x_next_list.append(sol[1:])\n",
    "\n",
    "plt.xlabel(r'$x_1$',size=25)\n",
    "plt.ylabel(r'$x_2$',size=25)\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0, 0.5, '$x_2$')"
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## single trajectory\n",
    "data_st_X = np.vstack(x_list[:1])\n",
    "data_st_Y = np.vstack(x_next_list[:1])\n",
    "\n",
    "\n",
    "# plot\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot([data_st_X[:,0],data_st_Y[:,0]],\n",
    "         [data_st_X[:,1],data_st_Y[:,1]],'o-',alpha=0.3)    \n",
    "\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n",
    "\n",
    "plt.xlabel(r'$x_1$',size=25)\n",
    "plt.ylabel(r'$x_2$',size=25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0, 0.5, '$x_2$')"
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## two trajectories\n",
    "data_2t_X = np.vstack(x_list[:2])\n",
    "data_2t_Y = np.vstack(x_next_list[:2])\n",
    "\n",
    "# plot\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot([data_2t_X[:,0],data_2t_Y[:,0]],\n",
    "         [data_2t_X[:,1],data_2t_Y[:,1]],'o-',alpha=0.3)    \n",
    "\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n",
    "plt.xlabel(r'$x_1$',size=25)\n",
    "plt.ylabel(r'$x_2$',size=25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Applying DMD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "fitting 1 trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continuous eigenvalue =  (-0.04999999821162009+0j)\n",
      "continuous eigenvalue =  (-0.8793780367057831+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": "(-0.9, 0.9)"
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pydmd import DMD\n",
    "from pykoopman.regression import PyDMDRegressor \n",
    "\n",
    "regressor = DMD(svd_rank=2)\n",
    "# regressor = PyDMDRegressor(DMD(svd_rank=2))\n",
    "\n",
    "model_dmd = pk.Koopman(regressor=regressor)\n",
    "\n",
    "# training\n",
    "model_dmd.fit(data_st_X,data_st_Y)\n",
    "model_dmd.time['dt']=t[1]-t[0]\n",
    "for eigval in model_dmd.continuous_lamda_array:\n",
    "    print('continuous eigenvalue = ',eigval)\n",
    "\n",
    "# reconstruction\n",
    "x0 = data_st_X[0:1]\n",
    "x_tmp = x0\n",
    "x_pred_list = [x_tmp]\n",
    "for i in range(data_st_X.shape[0]-1):\n",
    "    x_tmp = model_dmd.predict(x_tmp)\n",
    "    x_pred_list.append(x_tmp)\n",
    "    \n",
    "X_pred = np.vstack(x_pred_list)\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot(X_pred[:,0], X_pred[:,1],'-ob',lw=4,label='pykoopman - dmd')\n",
    "plt.plot(data_st_X[:,0],data_st_X[:,1],'ro--',lw=2,label='train data')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "fitting 2 trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continuous eigenvalue =  (-0.0249999999747155+0j)\n",
      "continuous eigenvalue =  (-0.14586482575904705+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_dmd.fit(data_2t_X,data_2t_Y)\n",
    "\n",
    "x0 = data_2t_X[:1] \n",
    "x_tmp = x0\n",
    "x_pred_list = [x_tmp]\n",
    "for i in range(n_t-2):\n",
    "    x_tmp = model_dmd.predict(x_tmp)\n",
    "    x_pred_list.append(x_tmp)    \n",
    "X_pred_1 = np.vstack(x_pred_list)\n",
    "\n",
    "x0 = data_2t_X[n_t-1:n_t] \n",
    "x_tmp = x0\n",
    "x_pred_list = [x_tmp]\n",
    "for i in range(n_t-2):\n",
    "    x_tmp = model_dmd.predict(x_tmp)\n",
    "    x_pred_list.append(x_tmp)\n",
    "    \n",
    "X_pred_2 = np.vstack(x_pred_list)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot(X_pred_1[:,0], X_pred_1[:,1], '-b', lw=4, label='pykoopman - kdmd 1 ')\n",
    "plt.plot(data_2t_X[:n_t-1,0], data_2t_X[:n_t-1,1], 'r--', lw=2, label='true 1 ')\n",
    "\n",
    "plt.plot(X_pred_2[:,0], X_pred_2[:,1], '-c', lw=4, label='pykoopman - kdmd 2 ')\n",
    "plt.plot(data_2t_X[n_t-1:,0], data_2t_X[n_t-1:,1], 'y--', lw=2, label='true 2')\n",
    "\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n",
    "\n",
    "\n",
    "# get eigenvalues\n",
    "for eigval in model_dmd.continuous_lamda_array:\n",
    "    print('continuous eigenvalue = ',eigval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conclusion: 1) vanilla DMD is not good for global linearization. 2) it cannot take more than 1 trajectory from highly nonlinear low-dimensional system (it will work for high-dimensional system where the number of harmonics is much less compared to system state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Applying KDMD"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, let's find out what should be the right hyperparameter for kdmd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scale =  0.0001\n",
      "scale =  0.0001603718743751331\n",
      "scale =  0.00025719138090593444\n",
      "scale =  0.0004124626382901352\n",
      "scale =  0.0006614740641230146\n",
      "scale =  0.0010608183551394483\n",
      "scale =  0.0017012542798525892\n",
      "scale =  0.0027283333764867696\n",
      "scale =  0.004375479375074184\n",
      "scale =  0.007017038286703823\n",
      "scale =  0.011253355826007646\n",
      "scale =  0.018047217668271703\n",
      "scale =  0.028942661247167517\n",
      "scale =  0.046415888336127774\n",
      "scale =  0.07443803013251689\n",
      "scale =  0.11937766417144358\n",
      "scale =  0.19144819761699575\n",
      "scale =  0.30702906297578497\n",
      "scale =  0.49238826317067363\n",
      "scale =  0.7896522868499725\n",
      "scale =  1.2663801734674023\n",
      "scale =  2.030917620904735\n",
      "scale =  3.257020655659783\n",
      "scale =  5.2233450742668435\n",
      "scale =  8.376776400682925\n",
      "scale =  13.433993325988988\n",
      "scale =  21.54434690031882\n",
      "scale =  34.55107294592218\n",
      "scale =  55.41020330009492\n",
      "scale =  88.86238162743408\n",
      "scale =  142.51026703029964\n",
      "scale =  228.54638641349885\n",
      "scale =  366.5241237079626\n",
      "scale =  587.8016072274912\n",
      "scale =  942.6684551178854\n",
      "scale =  1511.77507061566\n",
      "scale =  2424.462017082326\n",
      "scale =  3888.155180308085\n",
      "scale =  6235.507341273912\n",
      "scale =  10000.0\n"
     ]
    },
    {
     "data": {
      "text/plain": "<matplotlib.legend.Legend at 0x103205ba320>"
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pykoopman.regression import KDMD\n",
    "from sklearn.gaussian_process.kernels import RBF, DotProduct, ConstantKernel\n",
    "\n",
    "forward_backward=False\n",
    "svd_rank = 5\n",
    "tikhonov_regularization = 1e-12\n",
    "\n",
    "err_st_list = []\n",
    "err_2t_list = []\n",
    "err_mt_list = []\n",
    "scale_array = np.logspace(-4,4,40)\n",
    "for scale in scale_array:\n",
    "    regressor = KDMD(svd_rank=svd_rank, \n",
    "                     # kernel=DotProduct(sigma_0=scale),\n",
    "                     kernel=RBF(length_scale=np.sqrt(scale)),\n",
    "                     forward_backward=forward_backward,\n",
    "                     tikhonov_regularization=tikhonov_regularization)\n",
    "\n",
    "    model_kdmd = pk.Koopman(regressor=regressor)\n",
    "    \n",
    "    # single data\n",
    "    model_kdmd.fit(data_st_X,data_st_Y)\n",
    "    err_st = np.linalg.norm(model_kdmd.predict(data_st_X) - data_st_Y)\n",
    "    \n",
    "    # 2 trajectory data\n",
    "    model_kdmd.fit(data_2t_X,data_2t_Y)\n",
    "    err_2t = np.linalg.norm(model_kdmd.predict(data_2t_X) - data_2t_Y)\n",
    "    \n",
    "    # multiple data\n",
    "    # model_kdmd.fit(data_mt_X_for_train,data_mt_Y_for_train)\n",
    "    err_mt = 0 # np.linalg.norm(model_kdmd.predict(data_mt_X_for_train) - data_mt_Y_for_train)\n",
    "    # model_kdmd.fit(data_mt_X_for_train,data_mt_Y_for_train)\n",
    "    \n",
    "    # model.fit(sol)\n",
    "    # print(model.koopman_matrix.shape)\n",
    "\n",
    "    err_st_list.append(err_st)\n",
    "    err_2t_list.append(err_2t)\n",
    "    err_mt_list.append(err_mt)\n",
    "    \n",
    "    print('scale = ',scale)\n",
    "    \n",
    "plt.loglog(scale_array, err_st_list,'-o',label='1')\n",
    "plt.loglog(scale_array, err_2t_list,'-^',label='2')\n",
    "plt.loglog(scale_array, err_mt_list,'-s',label='m')\n",
    "plt.legend(loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "choose the model with best hyperparameter, clearly here it is **overfitting** because we only have one trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "optimal scale 1 =  228.54638641349885\n",
      "optimal scale 2 =  2424.462017082326\n"
     ]
    }
   ],
   "source": [
    "scale_st = scale_array[np.argmin(err_st_list)]\n",
    "regressor_st = KDMD(svd_rank=svd_rank, \n",
    "                 kernel=RBF(length_scale=np.sqrt(scale_st)),\n",
    "                 forward_backward=forward_backward,\n",
    "                 tikhonov_regularization=tikhonov_regularization\n",
    "                )\n",
    "\n",
    "scale_2t = scale_array[np.argmin(err_2t_list)]\n",
    "regressor_2t = KDMD(svd_rank=svd_rank, \n",
    "                 kernel=RBF(length_scale=np.sqrt(scale_2t)),\n",
    "                 forward_backward=forward_backward,\n",
    "                 tikhonov_regularization=tikhonov_regularization\n",
    "                )\n",
    "\n",
    "model_kdmd_st = pk.Koopman(regressor=regressor_st)\n",
    "model_kdmd_2t = pk.Koopman(regressor=regressor_2t)\n",
    "\n",
    "print('optimal scale 1 = ',scale_st)\n",
    "print('optimal scale 2 = ',scale_2t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1 trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continuous eigenvalue =  (-0.9779338545838757+0j)\n",
      "continuous eigenvalue =  (-0.49910554654684647+0j)\n",
      "continuous eigenvalue =  (-1.146364687825299e-07+0j)\n",
      "continuous eigenvalue =  (-0.025013364031557028+0j)\n",
      "continuous eigenvalue =  (-0.05078929436412745+0j)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_kdmd_st.fit(data_st_X,data_st_Y)\n",
    "\n",
    "x0 = data_st_X[:1] \n",
    "x_tmp = x0\n",
    "x_pred_list = [x_tmp]\n",
    "for i in range(n_t-2):\n",
    "    x_tmp = model_kdmd_st.predict(x_tmp)\n",
    "    x_pred_list.append(x_tmp)\n",
    "    \n",
    "X_pred = np.vstack(x_pred_list)\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot(X_pred[:,0], X_pred[:,1],'-b',lw=4,label='pykoopman - kdmd')\n",
    "plt.plot(data_st_X[:,0],data_st_X[:,1],'r--',lw=2,label='true')\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n",
    "\n",
    "# get eigenvalues\n",
    "for eigval in model_kdmd_st.continuous_lamda_array:\n",
    "    print('continuous eigenvalue = ',eigval)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validate Koopman eigenfunction with an unseen trajectory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 1.0, 'label is the continuous eigenvalue')"
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x0 = [0.2,-0.8]\n",
    "sol_unseen = odeint(slow_manifold, x0, t, args=(mu,lda))\n",
    "\n",
    "efun_index, linearity_error = model_kdmd_st.validity_check(t, sol_unseen)\n",
    "\n",
    "\n",
    "plt.figure()\n",
    "plt.scatter(efun_index,linearity_error )\n",
    "\n",
    "for i in range(len(efun_index)):\n",
    "    eigvals_c = np.log(np.diag(model_kdmd_st.lamda))/model_kdmd_st.time['dt']\n",
    "    plt.text(1e-1+1.0*efun_index[i],linearity_error[i],\n",
    "             \"{:.2f}\".format(eigvals_c[efun_index][i]))\n",
    "plt.yscale('log')\n",
    "plt.xlabel('index')\n",
    "plt.ylabel('linear evolution error in Koopman eigenspace')\n",
    "plt.title('label is the continuous eigenvalue')\n",
    "# plt.plot(model_kdmd_2t.eigenvalues_continuous[efun_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check out the validation error across 100 random unseen trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0, 0.5, 'linear evolution error')"
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "x0_array = np.random.rand(100,2)-0.5\n",
    "eigvals_c = np.log(np.diag(model_kdmd_st.lamda))/model_kdmd_st.time['dt']\n",
    "for x0 in x0_array:\n",
    "    sol_unseen = odeint(slow_manifold, x0, t, args=(mu,lda))\n",
    "    efun_index, linearity_error = model_kdmd_st.validity_check(t, sol_unseen)\n",
    "    \n",
    "    plt.scatter(eigvals_c[efun_index],linearity_error)\n",
    "    \n",
    "plt.xlabel('continuous eigenvalue')\n",
    "plt.ylabel('linear evolution error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2 trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "continuous eigenvalue =  -1.043123221391462\n",
      "continuous eigenvalue =  -0.6536012105988731\n",
      "continuous eigenvalue =  -1.8501593617281976e-06\n",
      "continuous eigenvalue =  -0.05000267048212399\n",
      "continuous eigenvalue =  -0.08628982133837682\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 600x600 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_kdmd_2t.fit(data_2t_X,data_2t_Y)\n",
    "\n",
    "x0 = data_2t_X[:1] \n",
    "x_tmp = x0\n",
    "x_pred_list = [x_tmp]\n",
    "for i in range(n_t-2):\n",
    "    x_tmp = model_kdmd_2t.predict(x_tmp)\n",
    "    x_pred_list.append(x_tmp)    \n",
    "X_pred_1 = np.vstack(x_pred_list)\n",
    "\n",
    "x0 = data_2t_X[n_t-1:n_t] \n",
    "x_tmp = x0\n",
    "x_pred_list = [x_tmp]\n",
    "for i in range(n_t-2):\n",
    "    x_tmp = model_kdmd_2t.predict(x_tmp)\n",
    "    x_pred_list.append(x_tmp)\n",
    "    \n",
    "X_pred_2 = np.vstack(x_pred_list)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(6,6))\n",
    "plt.plot(X_pred_1[:,0], X_pred_1[:,1], '-b', lw=4, label='pykoopman - kdmd 1 ')\n",
    "plt.plot(data_2t_X[:n_t-1,0], data_2t_X[:n_t-1,1], 'r--', lw=2, label='true 1 ')\n",
    "\n",
    "plt.plot(X_pred_2[:,0], X_pred_2[:,1], '-c', lw=4, label='pykoopman - kdmd 2 ')\n",
    "plt.plot(data_2t_X[n_t-1:,0], data_2t_X[n_t-1:,1], 'y--', lw=2, label='true 2')\n",
    "plt.xlim([-0.9,0.9])\n",
    "plt.ylim([-0.9,0.9])\n",
    "\n",
    "\n",
    "plt.legend(loc='best')\n",
    "plt.xlabel(r'$x_1$')\n",
    "plt.ylabel(r'$x_2$')\n",
    "\n",
    "# get eigenvalues\n",
    "model_kdmd_2t.time['dt']=t[1]-t[0]\n",
    "for eigval in np.diag(model_kdmd_2t.lamda):\n",
    "    print('continuous eigenvalue = ',np.log(eigval)/model_kdmd_2t.time['dt'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validate the learned Koopman eigenfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0.5, 1.0, 'label is the continuous eigenvalue')"
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "efun_index, linearity_error = model_kdmd_2t.validity_check(t, sol_unseen)\n",
    "\n",
    "eigvals_c = np.log(np.diag(model_kdmd_2t.lamda))/model_kdmd_2t.time['dt']\n",
    "plt.figure()\n",
    "plt.scatter(efun_index,linearity_error )\n",
    "\n",
    "for i in range(len(efun_index)):\n",
    "    plt.text(1e-1+1.0*efun_index[i],linearity_error[i],\n",
    "             \"{:.2f}\".format(eigvals_c[efun_index][i]))\n",
    "plt.yscale('log')\n",
    "plt.xlabel('index')\n",
    "plt.ylabel('linear evolution error in Koopman eigenspace')\n",
    "plt.title('label is the continuous eigenvalue')\n",
    "# plt.plot(model_kdmd_2t.eigenvalues_continuous[efun_index])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check out the validation error across 100 random unseen trajectories"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "Text(0, 0.5, 'linear evolution error')"
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "x0_array = np.random.rand(100,2)-0.5\n",
    "eigvals_c = np.log(np.diag(model_kdmd_2t.lamda))/model_kdmd_2t.time['dt']\n",
    "for x0 in x0_array:\n",
    "    sol_unseen = odeint(slow_manifold, x0, t, args=(mu,lda))\n",
    "    efun_index, linearity_error = model_kdmd_2t.validity_check(t, sol_unseen)\n",
    "    \n",
    "    plt.scatter(eigvals_c[efun_index],linearity_error)\n",
    "    \n",
    "plt.xlabel('continuous eigenvalue')\n",
    "plt.ylabel('linear evolution error')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Conclusion: 1) we can see -0.05 and -1 has very small validation error variance  2) it is likely that the one has largest variance is most likely to be the spurious mode"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Access the matrices related to Koopman operator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(5, 5)"
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_kdmd_st.A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(2, 5)"
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_kdmd_st.C.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": "(2, 5)"
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_kdmd_st.W.shape"
   ]
  }
 ],
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